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Scaling Higher-Order Graph Learning with Maximal Clique Complexes

arXiv 2605.31373 ↗First posted 29 May 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

Graph neural networks (GNNs) are limited to modeling pairwise interactions, while higher-order models based on cell complexes achieve greater expressivity but often suffer from poor scalability. We introduce simplified and factored cellular Weisfeiler Leman tests (sCWL and fCWL), which preserve the expressivity of the CWL test while improving computational efficiency. We further introduce the maximal clique complex, enabling scalable CWNs with reduced time and memory complexity while retaining strong empirical performance. To avoid explicit clique enumeration, we propose CliqueWalk, a biased random walk that samples maximal cliques and scales linearly with graph size. These contributions yield a scalable topological learning framework for higher-order graph representation.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 29 of its 56 references that are in the map. First posted on arXiv 29 May 2026.

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References · 29

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
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17 more
  1. 2019Provably Powerful Graph Networkscited by 385
  2. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  3. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  4. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  5. 2020GraphNorm: A Principled Approach to Accelerating Graph Neural Network Trainingcited by 116
  6. 2020Simplicial Neural Networkscited by 105
  7. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  8. 2020Cell Complex Neural Networkscited by 66
  9. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  10. 2015Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveyscited by 59
  11. 2022A Short Tutorial on The Weisfeiler-Lehman Test And Its Variantscited by 52
  12. 2021Generative hypergraph clustering: from blockmodels to modularitycited by 48
  13. 2019Alchemy: A Quantum Chemistry Dataset for Benchmarking AI Modelscited by 36
  14. 2023Generalized Simplicial Attention Neural Networkscited by 27
  15. 2024TopoX: A Suite of Python Packages for Machine Learning on Topological Domainscited by 22
  16. 2023CIN++: Enhancing Topological Message Passingcited by 14
  17. 2022Graph Neural Networks in Computer Vision -- Architectures, Datasets and Common Approachescited by 4

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